Nuclear Physics And Radioactivity Question 288
Question: The half-life of the isotope $ _{11}Na^{24} $ is 15 hrs. How much time does it take for $ \frac{7}{8}th $ of a sample of this isotope to decay [MP PET 1994]
Options:
A) 75 hrs
B) 65 hrs
C) 55 hrs
D) 45 hrs
Show Answer
Answer:
Correct Answer: D
Solution:
Undecayed isotope $ =\frac{3.2\times 10^{6}}{200\times 10^{6}\times 1.6\times {{10}^{-19}}}=1\times 10^{17} $
$ \therefore \frac{N}{N_{0}}={{( \frac{1}{2} )}^{t/T}}\Rightarrow ( \frac{1}{8} )={{( \frac{1}{2} )}^{t/15}}\Rightarrow \frac{t}{15}=3 $ or t =45 hours
BETA
